MULTIDIMENSIONAL AUTONOMOUS DIFFERENTIAL SYSTEM WITH UNIT MEASURE OF INSTABILITY AND MASSIVE PARTICULAR STABILITY

An example of non-one-dimensional autonomous differential system is constructed, in which, on the one hand, all solutions starting in the exterior of the unit ball, tend to zero with unlimited growth of time, and on the other hand, a relative measure of the initial conditions of those solutions that begin in the ball with a center at the zero and move away from it at a sufficient distance with increasing time, approaches arbitrary close to unity as the radius of the ball tends to zero. The nonlinear system constructed in this work also has a zero linear approximation along the zero solution.